In the last few weeks I've started to develop stretch marks on my inner upper arm area.

Does the Bio Oil advertised on tv work as well as it's portrayed? Also is there a way to prevent them while continuing to progress with my lifts?

Bio Oil will hydrate the skin and over time improve the appearance if the marks are not severe, but no it won't get rid of them.

You may or may not be able to prevent them, it could be hormonal ?

What you can do is to make sure you keep your body hydrated, lots of water, eat a diet high in vitamin c, zinc & protein.All are necessary for cell regeneration & maintaining collagen fibers.

Dry skin is more prone to stretch marks because collagen & elastin fiber require moisture to stay strong, so lots of stretch mark creams are just good moisturisers. Try massaging the marks with some shea butter, Almond oil, or vitamin E oil. Keep them moisturised daily!

Some people have had great result with derma rollers (as stated above) and laser treatments, but what works wonders for some might not work for you.
Remember the damage is done in the dermis so keep this in mind when looking at treatments.